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A009578
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Expansion of sinh(ln(1+x))/exp(x). Unsigned sequence gives degrees of (finite by nilpotent) representations of Braid groups.
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3
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0, 1, -3, 9, -34, 165, -981, 6853, -54804, 493209, -4932055, 54252561, -651030678, 8463398749, -118487582409, 1777313736045, -28437019776616, 483429336202353, -8701728051642219, 165332832981202009, -3306656659624040010
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| For the unsigned sequence, a(n)=n[2a(n-1)+3-n]/2, a(0)=0. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 24 2001
a(n) = (-1)^(n-1)/2*floor(n!*exp(1)+n-1), n>0. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 17 2002
The defining generating function simplifies to x(2+x)exp(-x)/[2(1+x)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2007
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MAPLE
| g:=(1/2)*x*(2+x)*exp(-x)/(1+x): gser:=series(g, x=0, 25): seq(factorial(n)*coeff(gser, x, n), n=0..20); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2007
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MATHEMATICA
| Sinh[ Log[ 1+x ] ]/Exp[ x ]
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PROG
| (MAGMA) f := function(n) nn := n; for i := 2 to n do nn := nn+Factorial(n)/(Factorial(n-i)*2); end for; return nn; end function;
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CROSSREFS
| A009578(n)=n[1+A000522(n-1)]/2 for n>0
Cf. A009132.
Sequence in context: A085686 A191412 A084756 * A067787 A130491 A149013
Adjacent sequences: A009575 A009576 A009577 * A009579 A009580 A009581
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KEYWORD
| sign,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net), Stephen P Humphries (steve(AT)math.byu.edu)
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EXTENSIONS
| Extended with signs Mar 15 1997 by Olivier Gerard.
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